Regularisation of AD is governed by section 257 in public company which talked about a General meeting only. So you can easily regularise your AD in the EGM before the AGM by following the procedure given in section 257. There is no doubt about the opinion above.

Hence in Pvt. Co., additional director can straight way show his intention in any GM regarding his regularization. If ord resolution is passed, he will be regular director.

But i have one question (related to the discussion going on) as Sec. 260 (Additional Director) and Sec. 257 is NA to Pvt. Co. - hence if additional director is appointed in Pvt. Co., can he be regularized in BoD meeting instead of GM?

It is not advisable to keep the appointing and regularising authority same even if the same is not dealt with by a specific section in case of a private company. Especially when the same can easily be regularised through a GM resolution in case of a private company practically.